Question

Find the derivative of y with respect to x, t, or θ, as appropriate
y = ln (cos (ln θ))
the answer is -(tan (lnθ)/θ)
i just dont know how to get that

Answer 1

So this is just a multiple chain rule so it becomes
\[\ln(v(u))\]\[v = \cos(u)\] \[u = \ln\]
so you get
\[(1/\cos(\ln \theta) )* (-\sin(\ln \theta) * (1/\theta)\] \[= -\tan(\ln \theta)/\theta \]

Answer 2

thank you